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Is Math an invention or a discovery?

Every person who loves math would , at some point of time come across this question.
If it is a discovery, what are the reasons? Providing examples from history does not prove the point! Was counting created by humans or was it borrowed from other creatures on this planet?
If it was an invention, what made the man transform from counting numbers orally to give a structure to it?

I'd say the theory behind the workings of the world to be physics instead of mathematics. Mathematics generalize and abstract the world further than physics; these generalizations must certainly be inventions, since there's no rigorous reason of why we should generalize them in this way.

Regarding definitions, I'd say a "discovery" to be something that can be rigorously reasoned (although it might take a fantastic leap of logic to think of that discovery before starting to reason it), and an "invention" to be something that can't be rigorously reasoned. "Rigorously reasoned" simply means following the rules of logic, just like all proofs must be rigorous.

Math is both invention and discovery. We just define axioms "arbitrarily" (Peano's axioms generate the natural numbers, for example). But we find that they mesh together beautifully, and we start actively discovering things that can be derived from them. It's invention that makes math to exist, but discovery that makes math an active subject.

Huh. That one is interesting. I'd say invention goes first; they invented an "infinite number of axioms" called the natural numbers (that \(1\) is a "single object", whatever that means, \(2\) follows \(1\), \(3\) follows \(2\), and so on), and then they discover the rules of addition perhaps, and perhaps the concepts of fractions and real numbers and elementary functions and calculus and more, until finally Peano makes this natural numbers more succinct by his axioms thus rigorously completing the base.

Invention (of natural numbers) goes first, but they expand both ways quickly; math is continuously invented while also being discovered.

firstly natural numbers existed in the sense that they occurred naturally .. !! for eg.. a shepherd who could guarantee that the number of sheep he took for grazing are exactly the same as he had before ; by having an account of the stones (he took originally the same number as sheep he had before). One stone in the pocket means that one sheep is in .. and as soon as all the stones are in his pocket he will be sure that the sheep are well in .. !! this accounts for thee counting you just mentioned .. and later on the man transformed it to a subject which had many applications .

To me Math is a discovery, just like magic squares and many other fascinating aspects of Math in our world. We discover Math because even if humans have not known of Math, Math still exists in our world, in nature. So how can we say we invented Math when we just got the knowledge of it from our world?

I think its is an invention at its base. As in creation of the mathematical "Universe". Once the basic rules are set, the rest becomes a discovery.

Extending the analogy, I say natural numbers map to our home, the place which we start "discovering" as kids. Rational numbers to our city and Real numbers to our country... And the higher concepts map to other planets and systems and galaxies..

well actually we have invented mathematics as in mathematics sometimes we can make some axiom and then find other deductions from it and these axioms can be anything.like as we study plane geometry,but actually there is nothing like a plane we just imagine it,in actual sense we use spherical geometry and its laws are very different from plane geometry.this is the difference between physics and mathematics